Protrusion Fourier Descriptor: Skeleton-based Representation of Open Curves

Eiki Tanaka¹*, Yoshiyasu Tamura², Masaki Hosoya³ and Toshihiko Shiroishi⁴

¹Department of Statistical Science, The Graduate University for Advanced Studies, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569, Japan
²The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569, Japan
³Department of Genetics, The Graduate University for Advanced Studies, Yata 1111, Mishima, Shizuoka 411-8540, Japan
⁴Mammalian Genetics Laboratory, National Institute of Genetics, Yata 1111, Mishima, Shizuoka 411-8540, Japan
*E-mail address: etanaka@ism.ac.jp

(Received July 14, 2008; Accepted October 17, 2008)

Keywords: Open Curve, Fourier Descriptor, Skeleton, Logistic Regression, Generalized Information Criterion

Abstract. If only some part of an object outline is of the matter of interest in statistical shape analysis, an appropriate open-curve descriptor is needed and tangent Fourier descriptor (TFD, also called P-type Fourier descriptor) is one such example. However, the TFD amplifies high frequency noise. In this paper we propose protrusion Fourier descriptor (PFD), an open-curve descriptor utilizing the skeletal information for an open curve, which is invariant under translation and rotation. Using regularized logistic regression model and generalized information criterion, we compare the PFD to the TFD in terms of capability to capture subtle variability of irregular shapes. The experiments with open curves extracted from nine inbred strains of mouse mandibular outlines have shown that different strains of data separate more clearly using the PFD than when using the TFD, and the PFD reflects inter-strain variability better.